Effect of MultiSubstitution on the Thermoelectric Performance of the

Article pubs.acs.org/IC

Effect of MultiSubstitution on the Thermoelectric Performance of the Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) System: Experimental and Theoretical Studies Gnu Nam,†,∥ Woongjin Choi,†,∥ Junsu Lee,† Seong-Ji Lim,† Hongil Jo,‡ Kang Min Ok,*,‡ Kyunghan Ahn,*,§ and Tae-Soo You*,† †

Department of Chemistry, Chungbuk National University, Cheongju, Chungbuk 28644, Republic of Korea Department of Chemistry, Chung-Ang University, Seoul 06974, Republic of Korea § School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea ‡

S Supporting Information *

ABSTRACT: The Zintl phase solid-solution Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) system with the cationic/anionic multisubstitution has been synthesized by molten Sn metal flux and arc-melting methods. The crystal structure of the nine title compounds were characterized by both powder and single-crystal X-ray diffractions and adopted the Ho11Ge10-type structure with the tetragonal space group I4/mmm (Z = 4, Pearson Code tI84). The overall isotypic structure of the nine title compounds can be illustrated as an assembly of three different types of cationic polyhedra sharing faces with their neighboring polyhedra and the three-dimensional cage-shaped anionic frameworks consisting of the dumbbell-shaped Sb2 units and the square-shaped Sb4 or (Sb/Ge)4 units. During the multisubstitution trials, interestingly, we observed a metal-tosemiconductor transition as the Ca and Ge contents increased in the title system from Yb11Sb10 to Ca9Yb2Sb7Ge3 (nominal compositions) on the basis of a series of thermoelectric property measurements. This phenomenon can be elucidated by the suppression of a bipolar conduction of holes and electrons via an extra hole-carrier doping. The tight-binding linear muffin-tin orbital calculations using four hypothetical structural models nicely proved that the size of a pseudogap and the magnitude of the density of states at the Fermi level are significantly influenced by substituting elements as well as their atomic sites in a unit cell. The observed particular cationic/anionic site preferences, the historically known abnormalities of atomic displacement parameters, and the occupation deficiencies of particular atomic sites are further rationalized by the QVAL value criterion on the basis of the theoretical calculations. The results of SEM, EDS, and TGA analyses are also provided.

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INTRODUCTION Thermoelectric (TE) materials can be used to convert the wasted heat from many different heat sources into electricity.1,2 Therefore, the TE power generators based on the TE materials has been regarded as one of the smart ways to recover wasted energy and eventually to provide a solution on a global energy overconsumption issue.3,4 The performance of TE materials is governed by a TE figure of merit ZT, expressed as σS2T/κ, where σ is the electrical conductivity, S is the Seebeck coefficient, T is the absolute temperature, and κ is the thermal conductivity.5 High σ and S as well as low κ are necessary to maximize ZT, but it is quite tricky to achieve due to the interdependence of these three parameters. Recently, some novel ways of improving ZT, such as nanostructure inclusions,6−9 electronic band structure engineering,10 and discoveries of TE materials with a very low thermal conductivity,11−13 have brought worldwide attention to the material chemistry as well as the materials science field. Among © 2017 American Chemical Society

many novel candidates for TE material applications, the Zintl phase is a relatively novel material and has proven its potentiality as a TE material on the basis of its complex crystal structures and semiconducting behavior.14−17 Therefore, the Zintl phase can be considered as an intrinsically suitable TE material to substantially enhance ZT.18 In recent years, a series of compounds belonging to the A11M10 (A = alkaline-earth metals, rare-earth metals; M = triels, tetrels, pnictogens) system have been intensively studied due to their interesting TE properties and magnetocaloric effects. In particular, a series of ternary and quaternary indide compounds including the RE11Ge8In2 (RE = Gd−Tm) system,19 the RE11Tt4In6 (RE = Y, La, Gd−Er; Tt = Si, Ge) system,20,21 and the RE11Ge4In6−xMx (RE = La, Ce; M = Li, Ge; x = 1, 1.96) system22 and Ce11Ge3.73(2)In6.2723 have been investigated on the Received: March 21, 2017 Published: May 30, 2017 7099

DOI: 10.1021/acs.inorgchem.7b00617 Inorg. Chem. 2017, 56, 7099−7110

Article

Inorganic Chemistry

Figure 1. SEM images of single crystals of the three title compounds. Nominal compositions and scale bars are shown. compounds, we exploited two different reaction methods: (1) the molten Sn metal flux reaction method and (2) the arc-melting method under a partial Ar atmosphere. In the molten Sn metal flux reactions, in which an excess amount of Sn metals were used as a nonactive flux, a series of reactions were carried out in a zirconia crucible (length = 4 cm, diameter = 2 cm) having the reactant mixture with a Ca/Yb/Sb/ Ge/Sn ratio of 11−x:x:10−y:y:75 (x = 2, 7, 9, 10; y = 1, 3). An excess amount of Sn metal was placed at the bottom as well as on the top of the reactant mixture. Then, each zirconia crucible was subsequently enclosed in a fused-silica jacket acting as a secondary reaction container. Each reactant mixture was heated to 1323 K at a rate of 473 K/h, kept there for 1 h, and then cooled to 1023 K at a rate of 543 K/ h. In the last stage of each reaction, the molten Sn metal was removed from the reactant mixture by instantaneous centrifugation at 1023 K. Large amounts of small needle- or bar-shaped single crystals showing metallic luster were successfully obtained (see Figure 1). The Sndoped compound was also synthesized by arc melting using a reactant mixture with a Ca/Yb/Sb/Sn ratio of 9:2:9.5:0.5 followed by annealing at 1023 K for 2 weeks. Although a preliminary SXRD refinement resulted in the chemical composition Ca9.53(2)Yb1.47Sb9.11(8)Sn0.48(8) with an R index of 2.36%, the abnormally large atomic displacement parameter (ADP) values at two Wyckoff 8h sites hindered us from reporting this result in a current article. To prepare large amounts of products for a series of physical property measurements, the title compounds were reproduced by arc melting. All of the products were air and moisture stable for at least up to 3 weeks. X-ray Diffraction. A total of nine title compounds in the Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) solidsolution system were characterized by powder X-ray diffraction (PXRD) and SXRD. PXRD patterns were obtained for all title compounds at room temperature using a Bruker D8 diffractometer equipped with an area detector and monochromatic Cu Kα1 radiation (λ = 1.54059 Å). The collection step size was set at 0.05° in the range of 15° ≤ 2θ ≤ 85° with a total exposure time of 1 h. The phase purities of the title compounds were checked by comparing the collected powder patterns with the simulated pattern of the Ho11Ge10-type phase. SXRD data were collected for four title compounds using a Bruker SMART APEX2 CCD-based diffractometer equipped with Mo Kα1 radiation (λ = 0.71073 Å) at room temperature except Ca1.43(4)Yb9.57Sb9.86(1), which was collected at 120 K. First, several silvery, lustrous, needle-/bar-shaped single crystals were picked up from each batch of crushed samples, and their crystal qualities were briefly checked by a rapid scan. After this, the best crystals were chosen for full data collection using Bruker’s APEX2 program.30 Data reduction, integration, and unit cell parameter refinements were conducted using the SAINT program,31 and SADABS was used to perform semiempirical absorption corrections based on equivalents.32 The entire sets of reflections of six selected compounds were in good agreement with the tetragonal crystal system, and the space group I4/ mmm (no. 139) was eventually chosen for those crystal structures adopting the Ho11Ge10-type phase. Detailed crystal structures were solved by direct methods and refined to convergence by full matrix least-squares methods on F2. The refined parameters include the scale factor, the atomic positions with anisotropic displacement parameters (ADPs), extinction coefficients, and occupancy factors of the Ca2+/ Yb2+, Sb3, and Sb3/Ge1 mixed sites.

basis of their structure−composition−magnetic property relationship. However, a series of isotypic binary and ternary pnictogen compounds with small amounts of triel or tetrel doping, which include the A11Pn10−xTx (A = Rb, Cs, Sr, Ba, Eu, Yb; Pn = Sb, Bi; T = Si, Ge, Sn) system,24−27 have been interrogated for their TE material applications. In particular, in a previous article about the A11Sb10 (A = Ca, Yb) system, Brown et al. claimed that if the solid-solution Zintl phase Ca11−xYbxSb10 was successfully prepared28 then the electrical property could be finely tuned from a metal to a semiconductor on the basis of the Ca2+/Yb2+ mixed ratio as in the solidsolution Ca1−xYbxZn2Sb2.29 Therefore, we first attempted to synthesize the ternary Zintl phase solid-solution Ca11−xYbxSb10 system by introducing various ratios of the Ca2+/Yb2+ mixture; then we also tried to apply the anionic Ge doping for Sb as well. In this article, we discuss our systematic experimental and theoretical investigations to understand the effect of multisubstitution using both cationic and anionic substitution on the TE performances of the title Ca11−xYbxSb10−yGez system. We also demonstrate that the tuning of the Ca2+/Yb2+ ratio provides a metal-to-semiconductor transition and the Ge doping for Sb effectively removes electron carriers, resulting in suppressing a bipolar conduction for a high S. Experimentally observed relatively larger ADP values at two particular Wyckoff 8h sites and some deficiencies of the Sb or Sb/Ge mixed site occupancies are rationalized by the QVAL values obtained from the theoretical approaches. The correlation between the measured TE properties including a metal-to-semiconductor transition and the effect of multisubstitution is nicely rationalized by a series of electronic structure calculations using the tight-binding linear muffin-tin orbital (TB-LMTO) method. The results of SEM, EDS, and TGA analyses are also provided.

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EXPERIMENTAL SECTION

Synthesis. All of the sample preparation processes were performed inside an Ar-filled glovebox with O2 and H2O contents below 0.1 ppm or inside an arc-melting furnace under vacuum. The reactant elements used were purchased from Alfa Aesar, and the list is as follows: Yb (ingot, 99.9%), Ca (shot, 99.5%), Sb (piece, 99.999%), and Ge (shot, 99.999%). The lightly tanned surfaces of Yb and Ca were cleaned by scraping with a scalpel or a metal brush in a glovebox before use in reactions. One of the title compounds, Ca9.55(3)Yb1.45Sb9.77(2), was serendipitously produced as a side product as we investigated the Ca5−xYbxAl2Sb6 system by the high-temperature reaction using a Nb ampule (length = 4 cm, diameter = 1 cm), and the Ho11Ge10-type structure was assigned for this compound on the basis of single-crystal X-ray diffraction (SXRD) measurements. Once a crystal structure was refined, we attempted to establish the solid-solution Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) system having the various mixed ratios of Ca2+ and Yb2+ as well as hole doping using Ge for Sb. To produce a single-phase product of the title 7100


Article

Inorganic Chemistry

Table 1. SXRD Data and Structure Refinement Results for the Ca11−xYbxSb10−yGez (1.29(3) ≤ x ≤ 9.57(4); 0.12(4) ≤ y ≤ 0.36(8); z = 0, 0.25(14)) System empirical formula crystal system space group unit cell dimensions (Å) volume (Å3) dcalcd (g/cm3) data/restraints/parameters R indices (I > 2σ(I))a R indices (all data)a goodness of fit on F2 largest diff. peak/hole (e/Å3)

Ca9.55(3)Yb1.45Sb9.77(2)

Ca5.07(5)Yb5.93Sb9.85(1)

Ca2.40(6)Yb8.60Sb9.88(4)

Ca1.43(4)Yb9.57Sb9.86(1)

Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14)

tetragonal I4/mmm (no. 139) a = 11.988(1) c = 17.259(2) 2480.4(6) 4.883 855/0/45 R1 = 0.0177 wR2 = 0.0369 R1 = 0.0188 wR2 = 0.0373 1.206 1.496/−1.245





a R1 = ∑∥F0| − |Fc∥/∑|F0|; wR2 = {∑[w(F02 − Fc2)/∑[w(F02)2]}1/2, where w = 1/[σ2F02+ (A − P)2 + B − P], in which P = (F02 + 2Fc2)/3 and A and B are weight coefficients.

During the structure refinements of the five SXRD data, the cationic A3 site and the anionic Sb3 site (both Wyckoff 8h) displayed relatively larger isotropic ADP values (Ueq), which were also observed in the Ca11−xSrxSb10 (x = 2.37, 7.34)33 and the Sr11−xBaxSb10 (x = 0, 6) systems25 and Yb11Sb10.34 In addition, the anionic Sb3 or Sb3/Ge1 sites were refined with some vacancies as reported for Yb11Sb9.3Ge0.5.27 More detailed results of these structural refinements will be discussed in Crystal Structures. In the last stage of a refinement cycle, atomic positions were standardized using STRUCTURE TIDY.35 Important crystallographic data, atomic positions with ADPs, and selected interatomic distances are shown in Table 1−3. Further details about each crystal structure can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (49) 7247-808-666, e-mail: crysdata@fiz-karlsruhe.de) under depository numbers CSD-432703 for Ca9.55(3)Yb1.45Sb9.77(2), CSD-432704 for Ca5.07(5)Yb5.93Sb9.85(1), CSD-432705 for Ca2.40(6)Yb8.60Sb9.88(4), CSD432706 for Ca 1 . 4 3 ( 4 ) Yb 9 . 5 7 Sb 9 . 8 6 ( 1 ) , and CSD-432707 for Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14). Electronic Structure Calculations. To understand the overall electronic structures of the title compounds including the correlation between chemical compositions and band gap sizes, a series of theoretical tight-bonding linear muffin-tin orbital (TB-LMTO) calculations with the atomic sphere approximation (ASA) were performed on the four different structural models using the Stuttgart TB-LMTO47 program.36−39 For a practical reason, we used idealized compositions for the four models as follows: Yb11Sb10, Ca2Yb9Sb10, Ca2Yb9Sb9Ge, and Ca9Yb2Sb9Ge. To apply a particular composition for each model except Yb11Sb10, subspace group P-4 (no. 81) was applied to three ternary models. Lattice parameters and atomic coordinates were extracted from the SXRD results, and detailed structural information for four models is provided in Table S1. The local density approximation was adopted to treat exchange and correlation. All relativistic effects, except spin−orbit coupling, were taken into account using a scalar relativistic approximation. In the ASA method, space is filled with overlapping Wigner−Seitz (WS) atomic spheres.36−39 The symmetry of the potential inside each WS sphere was considered spherical, and a combined correction was used to take into account the overlapping part. The radii of the WS sphere were obtained by requiring the overlapping potential to be the best possible approximation to the full potential and were determined by an automatic procedure.40 This overlap should not be too large because the error in kinetic energy introduced by the combined correction is proportional to the fourth power of the relative sphere overlap. The used WS radii are listed as follows: Yb = 1.675−2.265 Å and Sb = 1.682−1.834 Å for Yb11Sb10; Ca = 1.687−1.804 Å, Yb = 1.687−2.190 Å, and Sb = 1.707−1.856 Å for Ca2Yb9Sb10; Ca = 1.679−1.794 Å, Yb = 1.679−2.179 Å, Sb = 1.701−1.849 Å, and Ge = 1.648 Å for

Ca2Yb9Sb9Ge; and Ca = 1.676−1.874 Å, Yb = 1.875−2.181 Å, Sb = 1.732−1.876 Å, and Ge = 1.662 Å for Ca9Yb2Sb9Ge. The basis sets included 4s, 4p, and 3d orbitals for Ca; 6s, 6p, and 5d orbitals for Yb; 5s, 5p, 5d, and 4f orbitals for Sb; and 4s, 4p, and 4d orbitals for Ge. The Ca 4p, Yb 6p, Sb 5d and 4f, and Ge 4d orbitals were treated by the Löwdin downfolding technique.41 The k-space integration was conducted by the tetrahedron method,42 and the self-consistent charge density was obtained using 244, 314, 314, and 314 irreducible k points for Yb11Sb10, Ca2Yb9Sb10, Ca2Yb9Sb9Ge, and Ca9Yb2Sb9Ge in the Brillouin zone, respectively. Thermogravimetric Analysis. The thermal stability of Ca6Yb5Sb10 (nominal composition) was investigated by TGA using a TA Instruments SDT2960 thermal analyzer. The sample (about 20 mg) was enclosed in an alumina crucible, heated under a continuous nitrogen flow from room temperature to 1273 K at a rate of 10 K/min, and then cooled to room temperature naturally. As shown in Figure S1, Ca6Yb5Sb10 is thermally stable up to approximately 1100 K. Electrical Transport Properties. Seven samples in the title Ca11−xYbxSb10−yGez system were cut and polished into a rectangular shape (3 mm × 3 mm × 9 mm) for the electrical conductivity measurements. The longer direction coincides with the direction in which the electrical conductivity was measured. The electrical conductivity σ and the Seebeck coefficient S were measured simultaneously under a helium atmosphere from room temperature to 700 K using a ULVAC-RIKO ZEM-3 instrument system. Thermal Conductivities. Thermal diffusivity (D) was directly measured using seven disk-shaped samples in the title Ca11−xYbxSb10−yGez system under an inert atmosphere from room temperature to 700 K by a flash diffusivity method using a Netzsch LFA 457 MicroFlash instrument. In the flash diffusivity method, the front face of a disk-shaped sample is irradiated by a short laser burst, and the resultant temperature increase on the rear face is recorded and analyzed by an IR detector. The thermal conductivity κ was calculated from the equation κ = DCpρ, where ρ and Cp are the density and heat capacity of the sample, respectively. In this work, the Dulong−Petit value (3R/atom, where R is the gas constant) was used for Cp. The total thermal conductivity κtot was assumed to be the sum of the lattice κlatt and electronic κelec thermal conductivities. κelec was expressed using the Wiedemann−Franz law (κelec = LσT), where L is the temperaturedependent Lorenz number. An L value was estimated using the single parabolic band (SPB) model43 from the temperature-dependent Seebeck coefficient, which was based on the assumption of acoustic phonon scattering. Finally, κlatt was calculated from the relationship κlatt = κtot − κelec. EDS and SEM Analysis. Elemental analysis by energy-dispersive X-ray spectroscopy (EDS) and images of selected single crystals were taken using an ULTRA Plus field-emission scanning electron 7101


Article

Inorganic Chemistry

Table 2. Atomic Coordinates and Equivalent Isotropic Displacement Parameters (Ueqa) from the SXRD Refinements for the Ca11−xYbxSb10−yGez (1.29(3) ≤ x ≤ 9.57(4); 0.12(4) ≤ y ≤ 0.36(8); z = 0, 0.25(14)) System atom

a

Wyckoff site

A1b A2b A3b A4b Sb1 Sb2 Sb3 Sb4 Sb5

16n 16n 8h 4e 16m 8j 8h 4e 4d


16n 16n 8h 4e 16m 8j 8h 4e 4d


16n 16n 8h 4e 16m 8j 8h 4e 4d


16n 16n 8h 4e 16m 8j 8h 4e 4d

A1b A2b A3b A4b Sb1 Sb2 Sb3/Ge1 Sb4 Sb5

16n 16n 8h 4e 16m 8j 8h 4e 4d

occupation (Ca2+/Yb2+)

x

Ca9.55(3)Yb1.45Sb9.77(2) 0 0 0.3321(3) 0 0.2054(1) 0.1532(2) 0.1238(2) 0 0 Ca5.07(5)Yb5.93Sb9.85(1) 0.47(1)/0.53 0 0.38(1)/0.62 0 0.62(2)/0.38 0.3302(1) 0.42(2)/0.58 0 1 0.2056(2) 1 0.1523(2) 0.92(2) 0.1247(2) 1 0 1 0 Ca2.40(6)Yb8.60Sb9.88(4) 0.22(1)/0.78 0 0.15(2)/0.85 0 0.36(2)/0.64 0.3304(1) 0.19(2)/0.81 0 1 0.2058(2) 1 0.1517(2) 0.94(2) 0.1251(2) 1 0 1 0 Ca1.43(4)Yb9.57Sb9.86(1) 0.13(2)/0.87 0 0.09(2)/0.91 0 0.22(2)/0.78 0.3303(2) 0.09(2)/0.91 0 1 0.2059(2) 1 0.1510(1) 0.93(2) 0.1256(1) 1 0 1 0 Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14) 0.87(1)/0.13 0 0.85(1)/0.15 0 0.91(1)/0.09 0.3326(2) 0.85(1)/0.15 0 1 0.2049(1) 1 0.1532(2) 0.56(4)/0.24(4) 0.1250(5) 1 0 1 0 0.88(1)/0.12 0.84(1)/0.16 0.92(1)/0.08 0.85(1)/0.15 1 1 0.89(1) 1 1

y

z

Ueq (Å2)a

0.2527(2) 0.3384(2) 0.3321(3) 0 0.2054(1) 1/2 0.1238(2) 0 1/2

0.3114(2) 0.1029(2) 0 0.1685(2) 0.1741(1) 0 0 0.3683(2) 1/4

0.0158(3) 0.0127(2) 0.0556(8) 0.0180(5) 0.0165(1) 0.0115(1) 0.0258(2) 0.0116(2) 0.0080(1)

0.2525(2) 0.3376(2) 0.3302(1) 0 0.2056(2) 1/2 0.1247(2) 0 1/2

0.3113(1) 0.1025(1) 0 0.1679(2) 0.1741(1) 0 0 0.3700(2) 1/4

0.0185(3) 0.0156(2) 0.0415(7) 0.0195(5) 0.0187(2) 0.0164(3) 0.0280(5) 0.0147(3) 0.0122(3)

0.2523(2) 0.3370(2) 0.3304(1) 0 0.2058(2) 1/2 0.1251(2) 0 1/2

0.3115(1) 0.1025(1) 0 0.1673(2) 0.1743(1) 0 0 0.3710(2) 1/4

0.0137(2) 0.0117(2) 0.0333(5) 0.0152(4) 0.0126(2) 0.0113(3) 0.0229(5) 0.0099(3) 0.0064(3)

0.2523(2) 0.3365(2) 0.3303(2) 0 0.2059(2) 1/2 0.1256(1) 0 1/2

0.3117(1) 0.1025(1) 0 0.1675(2) 0.1743(1) 0 0 0.3722(2) 1/4

0.0078(2) 0.0071(2) 0.0207(4) 0.0099(4) 0.0081(2) 0.0088(3) 0.0154(5) 0.0062(4) 0.0044(4)

0.2526(2) 0.3386(2) 0.3326(2) 0 0.2049(1) 1/2 0.1250(5) 0 1/2

0.3114(2) 0.1027(2) 0 0.1702(1) 0.1734(1) 0 0 0.3686(2) 1/4

0.0162(3) 0.0121(3) 0.0500(10) 0.0153(6) 0.0160(1) 0.0106(1) 0.0231(8) 0.0115(2) 0.0084(2)

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. bA = Ca2+/Yb2+ mixed site. Ca9Yb2Sb10, Ca6Yb5Sb10, and Ca2Yb9Sb10 (all nominal compositions), respectively.

microscope (SEM) system with an acceleration voltage of 30 kV (see Figure 1). Several needle-/bar-shaped single crystals were selected from different compounds synthesized using the Sn metal flux reactions. Selected single crystals were carefully mounted on the circumference of an aluminum puck with double-sided conducting carbon tape in an Ar-filled glovebox. EDS analysis indicated Ca 10.13 Yb 1.74Sb 9.12 , Ca6.50 Yb 5.22Sb 9.27 , and Ca2.99 Yb 8.89Sb 9.01 for

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RESULTS AND DISCUSSION

Crystal Structures. The Zintl phase solid-solution compounds with the mixed cations of Ca2+ and Yb2+ in the Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) system 7102


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Inorganic Chemistry

Table 3. Selected Bond Distances for the Ca11−xYbxSb10−yGez (1.29(3) ≤ x ≤ 9.57(4); 0.12(4) ≤ y ≤ 0.36(8); z = 0, 0.25(14)) System bond distance (Å)

a

atomic pair

Ca9.55(3)Yb1.45Sb9.77(2)

Ca5.07(5)Yb5.93Sb9.85(1)

Ca2.40(6)Yb8.60Sb9.88(4)

Ca1.43(4)Yb9.57Sb9.86(1)

Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14)

A1−Sb1 (×4)a A1−Sb1 (×2)a A2a−Sb1 (×4) A2−Sb3 (×8)a A2−Ge1 (×6)a A3−Sb1 (×2)a A3−Sb3a A4−Sb1 (×4)a A4−Sb3 (×4)a A4−Ge1 (×4)a Sb1−Sb1 Sb1−Sb3 (×2) Sb3−Sb3 (×2) Sb3−Ge1 (×4) Ge1−Ge1 (×2)

3.464(2) 3.577(2) 3.180(2) 3.460(2)

3.461(2) 3.570(2) 3.177(2) 3.444(2)

3.455(2) 3.559(2) 3.168(2) 3.430(2)

3.445(2) 3.545(2) 3.154(2) 3.411(2)

3.694(2) 3.535(3) 3.483(2) 3.586(1)

3.671(2) 3.480(3) 3.484(2) 3.584(2)

3.668(1) 3.469(2) 3.479(2) 3.574(1)

3.652(1) 3.447(2) 3.469(1) 3.567(1)

3.027(2) 3.308(2) 2.967(1)

3.018(2) 3.301(1) 2.988(2)

3.007(2) 3.298(1) 2.990(2)

2.991(2) 3.282(1) 2.991(2)

3.472(2) 3.589(1) 3.180(2) 3.460(2) 3.53(3) 3.696(2) 3.523(9) 3.478(2) 3.625(5) 3.47(5) 3.058(2) 3.286(4) 3.001(13) 2.82(7) 2.62(14)

A = Ca2+/Yb2+ mixed site.

Figure 2. Schematic illustration showing an assembly of structural moieties to form a crystal structure of the Ca11−xYbxSb10−yGez system. (a−c) Three different types of coordination polyhedra centered on three isolated Sb atoms and (d) the 3D anionic frameworks formed by the dumbbell site and square site Sb atoms. (e) The overall crystal structure is depicted by a combination of ball-and-stick and polyhedra representations. The dumbbell sites and square sites in the 3D frameworks are highlighted in cyan and orange, respectively.

located at Wyckoff 16m and 8h, respectively.22,23 The local geometry of each Sb site can be expressed as the one-squareface-capped antisquare prism (Wyckoff 4e), the two-rectangular-face-capped trigonal prism (Wyckoff 8j), and the fourtriangular-face-capped tetrahedron (Wyckoff 4d). These three types of polyhedra share their triangular or rectangular faces with neighboring polyhedra, resulting in a closely packed complex crystal structure (Figure 2e). Moreover, the cageshaped 3D anionic frameworks (Figure 2d) can be considered to be a cross-linked combination of the dumbbell-shaped Sb2 units (Wyckoff 16m) and the square-shaped Sb4 or (Sb/Ge)4 units (Wyckoff 8h).22 Interestingly, during the structure refinement, the cationic A3 site and the anionic Sb3 site (both Wyckoff 8h) in the four of ternary compounds displayed relatively larger ADPs (Ueq) values. These two 8h sites were historically known for their large Ueq values in the Ca11−xSrxSb10 (x = 2.37, 7.34)33 and

was successfully synthesized by conventional high-temperature solid-state reaction methods and characterized by both PXRD and SXRD analyses. A total of nine title compounds crystallized in the tetragonal space group I4/mmm (Z = 4, Pearson Code tI84) and adopted the Sm11Ge4In6-type structure,44 which is considered to be an ordered version of the binary Ho11Ge10type structure (Figure 2e).45 There are nine crystallographically independent atomic sites in a unit cell, including four cationic sites occupied by a mixture of Ca2+/Yb2+ and five anionic sites occupied by Sb or a mixture of Sb/Ge. The overall isotypic crystal structures of the nine title compounds can be described as an assembly of the three different types of cofacial coordination polyhedra, each of which is centered on three different isolated Sb atoms located at the Wyckoff 4e, 8j, and 4d sites (See Figure 2a−c), respectively, and the three-dimensional (3D) cage-shaped anionic framework formed by Sb and the Sb/Ge mixed site 7103


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Figure 3. Four cationic sites observed in Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14). Each site is illustrated as a coordination polyhedron formed by seven or nine Sb or the Sb3/Ge1 mixtures. Selected interatomic distances are also displayed.

Table 4. Site Volume and QVAL Values for Each Atomic Site of Ca11Sb10 atom

Ca1

Ca2

Ca3

Ca4

Sb1

Sb2

Sb3

Sb4

Sb5

Wyckoff site volume (Å3) QVAL

16n 57.67 1.684

16n 48.41 2.035

8h 59.75 1.557

4e 76.34 3.015

16m 86.60 4.928

8j 57.55 5.272

8h 89.83 4.837

4e 79.01 5.583

4d 57.20 5.548

Sr11−xBaxSb10 (x = 0, 6) systems25 and Yb11Sb10.34 In addition, the occupancy refinement revealed that the Sb3 sites are refined with approximately 6−11% vacancies among our title compounds as shown in Table 2. In particular, the two holedoping quaternary compounds containing Ge substitutions for Sb3 still showed some vacancies at the Sb3/Ge1 mixed sites as well. To allow vacancies at this mixed site, we followed the refinement procedure described in an earlier article about Yb11Sb9.3Ge0.5.27 Thus, we confirm that some vacancies exist at the anionic Wyckoff 8h site, whether the site is occupied by only Sb or the mixture of Sb/Ge. However, for the cationicmixed A3 sites, we were not able to clarify whether there were some vacancies to maintain the charge balance of the title compounds, unlike an earlier report by Prof. Ganguli.33 These kinds of relatively larger ADPs and the deficiencies of occupation at two Wyckoff 8h sites were not observed in the RE11Ge8In2 (RE = Gd−Tm),19 RE11Tt4In6 (RE = Y, La, Gd−Er; Tt = Si, Ge),20,21 and RE11Ge4In6−xMx (RE = La, Ce; M = Li, Ge; x = 1, 1.96) systems22 and Ce11Ge3.73(2)In6.27.23 Thus, we suspect anionic pnictogen elements as the cause of these abnormalities. The observed site preference of Ge toward the anionic Wyckoff 8h site in our Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14) will be further discussed in Cationic and Anionic Site Preference. The four Ca2+/Yb2+ mixed cationic sites can be described as coordination polyhedra surrounded by seven or nine anionic sites as shown in Figure 3. Quaternary Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14) is used as a representative of the isotypic title compounds. Both of the A1 and A3 sites are surrounded by seven anionic sites forming distorted pentagonal bipyramids. Although interatomic distances between a central cationic site and seven surrounding anionic sites range from 2.938(5) to 3.716(1) Å in those two pentagonal bipyramids, the site volumes of the A1 and the A3 sites should be quite similar to each other on the basis of an approximate Ca11Sb10 (see Table 4). However, the A2 and A4 sites are surrounded by seven and nine anionic sites forming a two-edge monocapped square pyramid and a two-edge bicapped square pyramid, respectively. In particular, the A4 site shows the largest site volume of 74.34 Å3 among these cationic sites. Interestingly,

two cationic elements Ca2+ and Yb2+ show a clear site preference over four available cationic sites, where the highest Ca2+ occupancy is observed at the A3 site as plotted in Figure 4.

Figure 4. Partial occupancies of Ca at four different cationic sites in four ternary compounds.

The site preference of any particular element can mostly be rationalized either by the size factor on the basis of a site volume or the electronic factor on the basis of a QVAL value.46 According to our comprehensive theoretical investigations, the experimentally observed site preference of Ca2+ can be nicely elucidated by the electronic factor. Detailed discussions about this cationic site preference are provided in Cationic and Anionic Site Preference. Cationic and Anionic Site Preference. We have attempted to introduce simultaneous multisubstitutions using a cationic Yb for Ca and an anionic Ge or Sn for Sb to a binary compound Ca11Sb10. During these trials, as briefly mentioned earlier, we clearly observed particular site preferences of cations as well as anions. In general, any atomic site preference can be explained either by the size factor on the basis of the size matches between a central atom and the surrounding local 7104


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the Allred−Rochow scale),47 the observed site preference of Ca2+ can readily be elucidated by the QVAL value criterion. It is noteworthy that in two reported isotypic systems Ca11−xSrxSb1033 and Sr5Ba6Sb1025 including the Ca2+/Sr2+ or Sr2+/Ba2+ mixed cations, respectively, the cationic site preference seems to be mainly influenced by the size factor criterion due to the large size differences between two elements (r(Ca2+) = 1.06 Å, r(Sr2+) = 1.21 Å, r(Ba2+) = 1.38 Å),51 unlike our current work. This result implies that when the size factor and the electronic factor conflict and the size difference between two elements is sufficiently large, then the site preference mostly follows the size factor criterion. Electronic Structures and Chemical Bonding. A series of theoretical calculations have been conducted to understand the following issues brought about by this Zintl phase solidsolution Ca11−xYbxSb10−yGez system: (1) the cation-substitution effect on the electronic structure of Yb11Sb10 vs Ca2Yb9Sb10, (2) the anion-doping effect on the electronic structure of Ca2Yb9Sb10 vs Ca2Yb9Sb9Ge, and (3) the influence of Ca2+/Yb2+ mixed ratio Ca2Yb9Sb9Ge vs Ca9Yb2Sb9Ge. Therefore, the four different model structures having idealized compositions of Yb11Sb10, Ca2Yb9Sb10, Ca2Yb9Sb9Ge, and Ca9Yb2Sb9Ge were exploited for a series of theoretical calculations using the TB-LMTO-ASA method. First, to investigate an effect of the cationic Ca substitution for Yb in Yb11Sb10, we conducted calculations and compared the resultant electronic structures of Yb11Sb10 and Ca2Yb9Sb10 as shown in Figure 5a,b. The overall shapes of two total DOS (TDOS) curves and the distributions of partial DOS (PDOS) curves resemble one another, and some DOS magnitudes at the Fermi level (EF) represent the metallic conduction of these two models. This similarity of the two DOS curves implies that a Ca substitution for Yb hardly influences the location and size of the band gap or the corresponding electrical conductivity of Ca2Yb9Sb10. The results of these theoretical calculations are consistent with the metallic conductivities of the two compounds as shown in Figure 7a. Second, the electronic structure of Ca2Yb9Sb10 is further compared with that of multisubstituted Ca2Yb9Sb9Ge (Figure 5c), including Ge at the Wyckoff 8h site. Interestingly, in the DOS curve of Ca2Yb9Sb9Ge, EF is located at a pseudogap showing a significantly decreased DOS value. A new EF location can surely be attributed to a reduced number of valence electrons from 72/formula unit in Ca2Yb9Sb10 to 71/formula unit in Ca2Yb9Sb9Ge. However, the decreased DOS value at EF should be further explained by the chemical bonding of two models based on the COHP curves.52 Thus, we plotted three different COHP curves for Ca2Yb9Sb10 and Ca2Yb9Sb9Ge in Figure 6a,b, respectively: (1) a COHP curve for the dumbbellshaped Sb2 unit, (2) a COHP curve for the cross-linker combining the Sb2 dumbbell-shaped and Sb4 square-shaped units, and (3) a COHP curve for the square-shaped Sb4 unit. In particular, the large antibonding character of the Sb1−Sb3 (cross- linker) COHP in Ca2Yb9Sb10 becomes significantly smaller in the Sb1-Sb3/Ge1 COHP of Ca2Yb9Sb9Ge. In addition, the Sb3-Sb3 (squares) COHP of Ca2Yb9Ge showing antibonding character at EF moves up in the conduction band of Ca2Yb9Sb9Ge, and this eventually results in an optimized Sb3-Ge1 (“squares”) COHP at EF in Ca2Yb9Sb9Ge. Therefore, the decreased DOS value at EF in Ca2Yb9Sb9Ge should be attributed to a synergetic effect of two heterogeneous Sb1-Sb3/ Ge1 and Sb3-Ge1 interactions generated by a Ge substitution for Sb. In addition, the reduced metallic conductivity observed

coordination geometry or by the electronic factor on the basis of the correlation between the QVAL value of a particular atomic site and the electronegativity of an element occupying the site. In our multisubstituted q uaternary compound Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14), the Ge substitution occurs only at the Sb3 site (Wyckoff 8h) forming the square-shaped Sb4 unit among five available Sb sites. This type of Ge site preference can hardly be elucidated by the size factor given that a relatively smaller Ge (r(Ge) = 1.22 Å, r(Sb) = 1.38 Å)46 preferentially occupies the largest Sb3 site (site volume = 89.83 Å3) rather than the smallest Sb2 site (site volume = 57.55 Å3) (see Table 4 ). Instead, as we successfully demonstrated in the previous article about the RE11Ge4In6−xMx (RE = La, Ce; M = Li, Ge; x = 1, 1.96) system,22 the electronic-factor criterion based on the quantity called the QVAL value should be adopted to explain this phenomenon. Given that each QVAL value is evaluated by the summation of integrated electron densities inside each corresponding WS sphere, we should expect the element having the higher electronegativity to occupy the atomic site with the higher QVAL value. Some other successful examples include the EuZnxIn4−x (x = 1.1−1.2) system,47 the RE4LiGe4 (RE = La, Ce, Pr, and Sm) system,48 the Gd 5−x Y x Ge 4 (0 ≤ x ≤ 5) system, 49 and BaLi1.09(1)In0.91Ge2.50 According to QVAL values evaluated for binary compound Ca11Sb10 (Table 4), the Sb3 site (Wyckoff 8h) displays the smallest value among five anionic sites. This implies that as Ge with a relatively smaller electronegativity than that of Sb (Ge = 2.01 vs Sb = 2.05 in Pauling scale)47 is introduced into the title system, the substitution should occur at the Sb3 site. Interestingly, the same rationale can also be applied to the two previously reported isotypic systems containing Ge or Sn substituted for Sb or Bi in Yb11Sb9.3Ge0.527 and Yb11Bi5.2Sn4.824 reported by Prof. Kauzlarich and Prof. Grin, respectively. In these compounds, the site preference of Ge or Sn over the five available anionic sites cannot be explained by the size factor since the relatively smaller Ge or Sn (r(Ge) = 1.22 Å vs r(Sb) = 1.38 Å; r(Sn) = 1.40 Å vs r(Bi) = 1.52 Å)47 mostly prefers the largest Wyckoff 8h site. However, like our current work, the QVAL value criterion can successfully be applied to those systems on the basis of electronegativities (Ge = 2.01 vs Sb = 2.05; Sn = 1.96 vs Bi = 2.02 in the Pauling scale).47 In particular, once the Wyckoff 8h site is fully occupied by Sn in Yb11Bi5.2Sn4.8, then some additional Sn subsequently occupies the Wyckoff 16m and Wyckoff 8i sites, including the secondand the third-smallest QVAL values, respectively. Furthermore, as briefly mentioned in Crystal Structures, a cationic site preference is also observed among four cationic sites of the six SXRD data as well. In particular, the largest Ca2+ occupancy is observed at the A3 (Wyckoff 8h) site, whereas the smallest one is refined at the A4 (Wyckoff 4e) site. These site preferences cannot be rationalized by the size factor based on cationic sizes since the relatively smaller Ca2+ (r(Ca2+) = 1.06 Å vs r(Yb2+) = 1.08 Å)51 prefers the second largest A3 site (V = 59.36 Å3) among four cationic sites, whereas the smallest A2 site (V = 47.59 Å3) is least favored by Ca2+ as shown in Table 4. However, just like the anionic site preference, the electronic factor can nicely rationalize this refined cationic site preference. Both of the A3 and A1 sites, respectively, showing the smallest and the second-smallest QVAL values include the largest and the second-largest Ca2+ occupancies. Given that Ca has a smaller electronegativity than Yb (Ca = 1.04 vs Yb = 1.06 on 7105


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mixed ratio affects electronic structures. Interestingly, as shown in Figure 5d, a pseudogap region with a very small DOS value extends from EF down to −0.7 eV in Ca9Yb2Sb9Ge, whereas the DOS value starts to increase gradually just below EF in Ca2Yb9Sb9Ge. This difference can be attributed to the relatively lower electronegativity of Ca (Ca = 1.04 vs Yb = 1.06 on the Allred−Rochow scale)47 since Ca transfers electrons more readily to the anionic frameworks than Yb, resulting in the wider pseudogap region with a slight DOS value near EF. Given that the title compound Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14) has the closest composition to that of this structural model, which was successfully synthesized using a loaded composition of Ca9Yb2Sb7Ge3, we can consider that this theoretical result nicely represents the smallest electrical conductivity and the largest Seebeck coefficient of Ca 9 Yb 2 Sb 7 Ge 3 (nominal composition) among the seven measured compounds as shown in Figure 7a,b. This result also clearly rationalizes the metal-to-semiconductor transition caused by the multisubstitution of Ca and Ge for Yb and Sb in Yb11Sb10, respectively, resulting in Ca9Yb2Sb9Ge. Furthermore, we tried to understand the abnormally large ADP values observed at two Wyckoff 8h sites in our five SXRD data. The same patterns of large ADP values have been historically known for many isotypic compounds including the Ca11−xSrxSb10 (x = 2.37, 7.34)33 and the Sr11−xBaxSb10 (x = 0, 6) systems25 and Yb11Sb10.34 In particular, Brown et al. described the shape of a Sb ellipsoid at the Wyckoff 8h site as “flattened atoms” along the ab-plane direction.27 Interestingly, in our compounds, the Sb or Sb/Ge ellipsoid elongates toward the A3 site, whose abnormally large ellipsoid also points back to the Sb or Sb/Ge sites. During the QVAL value evaluation using an isotypic Ca11Sb10, we revealed that both of the two Wyckoff 8h sites displayed the lowest QVAL values among four cationic sites and five anionic sites, respectively. These indicate that two Wyckoff 8h sites intrinsically tend to include relatively smaller integrated electron densities, and thus, the elements occupying these sites tend to build the relatively weaker interatomic interactions with their surroundings. Therefore, the elements located at these two sites oscillate more readily and result in larger ADP values than do other elements. The deficiencies in Sb or Sb/Ge at the anionic Wyckoff 8h site can also be elucidated by this relatively smaller QVAL value as well. As the anionic Wyckoff 8h site is occupied by relatively lighter elements, such as Ge or In in the Ce11Ge3.73(2)In6.2723 and RE11Ge4In6−xMx (RE = La, Ce; M = Li, Ge; x = 1, 1.96) systems,22 the site can fully accommodate those lighter elements with the ADP value in the same range as elements in other anionic sites. However, as the site is occupied by a relatively heavier pnictogen, such as Sb or Bi, the Wyckoff 8h site should tend to leave some vacancies.27,33 Thermoelectric Properties. To investigate the multisubstitution effect on the TE properties of the solid-solution Ca11−xYbxSb10−yGez system, a series of TE property measurements were performed for the seven title compounds: one binary, three ternaries with the Ca2+/Yb2+ mixed cation, and three quaternaries with the Ca2+/Yb2+ mixed cation as well as Ge doping. Since we have attempted to alleviate the compensating effects of electrons and holes by introducing an extra hole carrier via Ge doping for Sb, we expected to induce a transition from a metal to a heavily doped semiconductor and eventually the fine-tuning of electrical transport properties. It is noteworthy that seven measured compounds are labeled with nominal compositions in Figures 7 and 8 for convenience.

Figure 5. TDOS and PDOS curves of four hypothetical structure models. EF (dashed vertical line) is shown as the energy reference (0 eV). Color codes are as follows: TDOS (bold black outline), Ca PDOS (gray region), Yb PDOS (magenta region), Sb PDOS (darkcyan region), and Ge PDOS (orange region).

in an electronic structure of Ca2Yb9Sb9Ge is in very good agreement with that measured experimentally as illustrated in Figure 7a. It is worth noting that the structural model for Ca2Yb9Sb9Ge includes only one type of square at the Wyckoff 8h site containing an alternating arrangement of Sb and Ge (Sb−Ge−Sb−Ge), which is expected to resemble an actual local arrangement. As we conducted another calculation for a structure model containing two types of squares (Ge4 and Sb4), the overall TDOS shape was nearly identical to that of Ca2Yb9Sb10 representing a metallic conductivity with some DOS values at EF (Figure S2). Thus, we conclude that the alternating arrangement of Sb and Ge at the Wyckoff 8h site, which generates two types of heterogeneous interactions Sb3Ge1 (squares) and Sb1-Sb3/Ge1 (cross-linkers), is essential to the reduced DOS value at EF and eventually resembles an actual local atomic arrangement. Finally, we compared TDOS of a Yb-rich Ca2Yb9Sb9Ge with that of a Ca-rich Ca9Yb2Sb9Ge to see whether the Ca2+/Yb2+ 7106


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Figure 6. Three COHP curves from two structural models: (a) Ca2Yb9Sb10 and (b) Ca2Yb9Sb9Ge. In the −COHP curves, the positive area with a “+” sign indicates the bonding interactions, whereas the negative area with a “−” sign represents the antibonding interactions. Detailed explanations are given in the text.

Figure 7. Temperature-dependent (a) electrical conductivity σ and (b) Seebeck coefficient S of the seven title compounds measured over the temperature range of 300−700 K.

amount of Ge doping in two other quaternary compounds Ca9Yb2Sb9Ge and Ca2Yb9Sb9Ge (nominal compositions) can also be smaller than the loaded Ge contents. Figure 7a shows the temperature-dependent electrical conductivities σ of the seven title compounds. Room temperature (RT) σ values of Ca 11 Sb 10 , Ca 9 Yb 2 Sb 10 , Ca6Yb5Sb10, and Ca2Yb9Sb10 are ca. 6, 388, 497, and 1563 S/

Among the three Ge-doped quaternary compounds, we confirmed a chemical composition of Ca9.71(3)Yb1.29Sb9.64(8)Ge0.25(14) for the sample Ca9Yb2Sb7Ge3 (nominal composition) on the basis of SXRD data. This implies that there should be a solubility limit of Ge doping for Sb in the A11Sb10 (A = Ca, Yb) system, which was already mentioned in an earlier article.27 Therefore, we assume that the 7107


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Figure 8. Temperature-dependent (a) total thermal conductivity κtot and (b) figure of merit ZT of the seven title compounds measured over the temperature range of 300−700 K.

cm, respectively. As can be expected, σ increases with increasing Yb content. The σ of Ca11Sb10 and Ca9Yb2Sb10 increase with increasing temperature, indicating typical semiconducting behavior, whereas that of Ca2Yb9Sb10 decreases with increasing temperature, proving a metallic conduction. The σ of Ca6Yb5Sb10 hardly shows any noticeable change within this temperature range. This result reveals that the transition between a metal and a semiconductor is tunable as well as reversible as a function of the amount of Yb in the Ca11−xYbxSb10−yGez system. Furthermore, as more Ge replaces Sb in the system, the overall σ of each compound decreases. For instance, RT σ values decrease from ca. 388 to 95 and to 1 S/cm as the amount of Ge increases from Ca9Yb2Sb10 to Ca9Yb2Sb9Ge and to Ca9Yb2Sb7Ge3, respectively. The same trend of σ reduction is also observed from ca. 1563 to 883 S/ cm for Ca2Yb9Sb10 and Ca2Yb9Sb9Ge, respectively. The temperature dependence of the Seebeck coefficient S of the seven compounds is nicely shown in Figure 7b. The overall S values of the three ternary compounds without the Ge doping are quite small in the measured temperature range: ca. 1−21 μV/K at 300 K and 14−17 μV/K at 700 K. These small S values are presumably due to the compensating behavior of holes and electrons in these compounds. This type of bipolar conduction is known to cause low S values with a weak temperature dependence. To achieve the higher S value (>100 μV/K) for the more suitable TE materials, a single type of electrical conduction by either electrons or holes is required for this system, and this can be realized by removing either one of the charge carriers through incorporation of the fourth element. Therefore, we attempted to introduce an extra hole carrier via Ge doping for Sb, resulting in the Ca11−xYbxSb10−yGez system, and we expected to suppress the bipolar conduction via one less electron than in the Ca11−xYbxSb10 system. During these trials, very surprisingly, we observed a significant enhancement of the S value up to ca. 78 μV/K at 700 K in Ca9Yb2Sb7Ge3 (ca. 15 μV/K at 700 K in Ca9Yb2Sb10). This demonstrates that an optimal amount of Ge doping can effectively eliminate electron charge carriers, which are responsible for compensated small S values and eventually improve the S value. The RT total thermal conductivities κtot of the binary and ternary compounds range between ca. 0.62 and 1.75 W/mK as

shown in Figure 8a. Given that the calculated Lorenz number L based on single parabolic band (SPB) model43 is nearly the same as a metallic value of ca. 2.42 × 10−8 V2/K2, regardless of temperature, the estimated RT lattice thermal conductivities κlatt of those are between ca. 0.34 and 0.78 W/m K (Figure S3). The κlatt values of Ca-rich compounds are almost the same as the κtot values due to their low σ, and all title compounds have a κlatt value of less than ca. 1.25 W/mK, which should be attributed to an intrinsically complex crystal structure of Ca11−xYbxSb10 compounds with multiple types of cations and anions, such as Ca2+, Yb2+, the Sb4 square unit, and the Sb2 dumbbell unit, and point-defect scattering of phonons by the solid solution of Ca11Sb10 with Yb11Sb10. Interestingly, the Carich compounds have κlatt values comparable to those of the Ybrich compounds, though the atomic weight of Ca is much smaller than that of Yb (40.08 g/mol vs 173.05 g/mol). Typically, TE materials with heavy elements display a κlatt value that is smaller than that of light elements mainly due to the lower phonon velocity of the formers. Doping with Ge resulting in the quaternary Ca11−xYbxSb10−yGez system increases the κlatt values in this work, which is different from a previous study on Yb11Sb9.3Ge0.5 with a smaller κlatt than that for Yb11Sb10.27 Such a discrepancy may be caused by different sample preparation processes (arc melting vs ball milling followed by hot pressing27). Finally, the temperature-dependent dimensionless figure of merit ZT of the Ca11−xYbxSb10−yGez system increases with increasing temperature (Figure 8b). Among the title compounds, Ca2Yb9Sb9Ge exhibits the highest ZT of ca. 0.01 at 700 K, although its absolute value is still quite low. However, this indicates that the Ge doping in Ca2Yb9Sb9Ge does not suppress bipolar conduction as effectively as in Ca9Yb2Sb7Ge3 with a low σ value. This proves that a good TE material should simultaneously have a high σ value with a high S value. As a consequence, a substantial enhancement of ZT of the Ca11−xYbxSb10−yGez system could be achievable by effectively suppressing the bipolar electrical conduction behavior coupled with heavy charge carrier doping through appropriate cationic/ anionic substitutions on the basis of band structure engineering as well as the subtle tuning of the mixed Ca2+/Yb2+ ratio. 7108


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CONCLUSION A series of a solid-solution Zintl phase Ca11−xYbxSb10−yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) systems have been successfully synthesized by molten Sn metal flux as well as arc-melting methods. The overall isotypic crystal structure was characterized by both PXRD and SXRD analyses and can be described as an assembly of the three different types of cofacial cationic polyhedral and the 3D anionic frameworks. In particular, the cage-shaped 3D anionic frameworks are considered as a cross-linked combination of the dumbbellshaped Sb2 units and the square-shaped Sb4 or (Sb/Ge)4 units. The title compounds displayed the relatively larger ADP value at both of the cationic and anionic Wyckoff 8h sites, and some vacancies were also observed at the anionic Wyckoff 8h sites. These abnormalities in the crystal structure refinements should be attributed to the relatively lower QVAL values, implying that the relatively smaller electron densities at the particular atomic sites result in relatively weaker interatomic interactions with the surroundings. The noticeable site preference of Ca2+ for the A3 and Ge for the Sb3 sites in the title compounds cannot be explained by the size factor but rather can be nicely rationalized by the electronic factor on the basis of QVAL values. The measured maximum ZT of Ca2Yb9Sb9G in the title system was still much lower than other practically known TE materials. However, we successfully demonstrated that the electrical conductivity is significantly affected by the cationic substitution, and in particular, at a certain mixed ratio between Ca2+ and Yb2+, the metal-to-semiconductor transition was observed. In addition, we also experimentally proved that the bipolar electrical conduction behavior can be reduced by the optimal amount of Ge doping via the elimination of electron charge carriers, which was eventually responsible for the improved S value. A series of theoretical calculations using four hypothetical structural models nicely elucidated that the experimentally observed metal-to-semiconductor transition as well as the reduced bipolar electrical conduction should be attributed to the multisubstitution effect of Ca and Ge for Yb and Sb, respectively, on the basis of the DOS values and the COHP analyses at EF. Therefore, on the basis of the current experimental and theoretical results, we believe that the enhanced ZT of the title system for a practical TE application can be achieved by an effective suppression of the bipolar electrical conduction behavior via an appropriate doping using the fourth element as well as subtle tuning of the Ca2+/Yb2+ ratio. These hypotheses are currently under investigation.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: + 82 (43) 261-2282. (T. -S. You) *E-mail: [email protected]. Phone: + 82 (2) 880-1530. (K. Ahn) *E-mail: [email protected]. Phone: + 82 (2) 820-5197. (K. M. Ok) ORCID

Kang Min Ok: 0000-0002-7195-9089 Kyunghan Ahn: 0000-0002-7806-8043 Tae-Soo You: 0000-0001-9710-2166 Author Contributions ∥

G.N. and W.C. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the Basic Science Research Program through the NRF funded by the Ministry of Science, ICT and Future Planning (2015R1A1A1A05027845, 2016R1A2A2A05005298), by the Creative Human Resource Training Project for Regional Innovation through NRF funded by the Ministry of Education (2014H1C1A1066874), and by a research grant from Chungbuk National University in 2014.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00617. Detailed structural information on the four hypothetical structural models, TGA diagram of Ca6Yb5Sb10, TDOS and PDOS of Ca2Yb9Sb9Ge, and temperature-dependent κlatt values (PDF) Accession Codes

CCDC 1548709 and 1548711−1548714 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/ cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. 7109


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Inorganic Chemistry

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